Positioning control method for drilling arm of bolt drilling rig
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摘要: 目前常用代数法和几何法实现锚杆钻车钻臂定位控制，存在效率低、有无解或多解情况、通用性差等问题。采用粒子群优化（PSO）算法进行机械臂定位控制具有编程简单、搜索性能强、容错性好等优势，但易陷入局部最优解。目前基于改进PSO算法的机械臂定位控制整体寻优效率较低，寻优时间过长。针对上述问题，在精英反向粒子群优化（EOPSO）算法基础上，引入混沌初始化、交叉操作、变异操作和极值扰动，设计了混沌交叉精英变异反向粒子群优化(CEMOPSO）算法。采用标准测试函数对PSO算法、EOPSO算法、交叉精英反向粒子群优化（CEOPSO）算法、CEMOPSO算法进行测试，结果表明CEMOPSO算法的稳定性、精度、收敛速度最优。建立了锚杆钻车钻臂运动模型，采用CEMOPSO算法进行钻臂定位控制，并在Matlab软件中对控制性能进行仿真研究，结果表明：在相同的迭代次数和误差精度约束条件下，采用CEMOPSO算法时钻臂位置误差和姿态误差从迭代初期即具有极快的收敛速度，且位置误差和姿态误差均小于其他3种算法，误差曲线较平稳，最大位置误差为0.005 m，最大姿态误差为0.005 rad；设定位置误差为1 mm、姿态误差为0.01 rad时，CEMOPSO算法的平均迭代次数为343，位置误差为0.1 mm、姿态误差为0.001 rad时平均迭代次数为473，在相同的定位精度条件下，CEMOPSO算法的收敛速度和稳定性优于其他3种算法，满足工程应用要求，且求解精度越高，其优越性越突出。Abstract: Algebraic and geometric methods are commonly used to realize drilling arm positioning control of bolt drilling rig. However, there are some problems such as low efficiency, no solution, multiple solutions, or poor universality. Using particle swarm optimization (POS) algorithm for positioning control of the drilling arm has the advantages of simple programming, strong search performance and good fault tolerance. But it is easy to fall into the local optimal solution. At present, the drilling arm positioning control based on improved PSO algorithm has low overall optimization efficiency and long optimization time. In order to solve the above problems, a chaotic crossover elite mutation opposition-based PSO (CEMOPSO) algorithm is designed by introducing chaos initialization, crossover operation, mutation operation and extreme value perturbation based on elite opposition-based PSO (EOPOS) algorithm. The method uses standard test functions to test PSO algorithm, EOPSO algorithm, CEOPSO algorithm and CEMOPSO algorithm. The results show that CEMOPSO has the best stability, precision and convergence speed. The motion model of the drilling arm of the bolt drilling rig is established. The CEMOPSO algorithm is used to control the drilling arm positioning. The simulation of the control performance is carried out in Matlab. The results show that under the same iteration times and error precision constraints, the position error and posture error of the drilling arm have a very fast convergence rate from the initial iteration when using the CEMOPSO algorithm. The position error and posture error are smaller than those of the other three algorithms. The error curve is smooth, and the maximum position error is 0.005 m and the maximum posture error is 0.005 rad. When the position error is 1 mm and the posture error is 0.01 rad, the average iteration number of the CEMOPSO algorithm is 343. When the position error is 0.1 mm and the posture error is 0.001 rad, the average iteration number is 473. Under the same positioning precision, the convergence speed and stability of the CEMOPSO algorithm are better than those of the other three algorithms. The results meet the requirements of engineering application. The higher the accuracy of the solution, the better it is.
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图 1 锚杆钻车钻臂结构
1−大臂摇摆关节；2−大臂俯仰关节；3−大臂伸缩关节；4−推进梁俯仰关节；5−推进梁摆动关节；6−推进梁回转关节；7−锚杆关节；8−推进梁伸缩关节。
Figure 1. Drilling arm structure of bolt drilling rig
图 3 基于CEMOPSO算法的锚杆钻车钻臂定位控制流程
Figure 3. Positioning control flow of drilling arm of bolt drilling rig based on chaotic crossover elite mutation opposition-based particle swarm optimization(CEMOPSO) algorithm
图 7 4种算法对钻臂定位控制的位置误差和姿态误差收敛曲线
Figure 7. Convergence curves of position errors and posture errors of drilling arm positioning control by use of four algorithms
图 8 4种算法对钻臂定位控制的位置误差和姿态误差曲线
Figure 8. Position error and posture error curves of drilling arm positioning control by use of four algorithms
图 9 4种算法在不同精度条件下的迭代次数
Figure 9. Iteration times of four algorithms under different precision conditions
表 1 锚杆钻车钻臂D−H参数
Table 1. D-H parameters of drilling arm of bolt drilling rig
关节 $ {\theta _j}/(^\circ ) $ $ {\alpha _j}/(^\circ ) $ $ {a_j}/{\rm{m}} $ $ {d_j}/{\rm{m}} $ 1 [45，135] 90 0.30 0 2 [−150，−60] −90 0 0 3 180 −90 0 [0，1.8] 4 [−120，−30] −90 0.35 0 5 [−135，−45] 90 0 0 6 [−270，90] −90 0.60 0.4 7 [−90，0] 90 0 0.8 8 90 −90 0 [0，2.5] 
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表 2 标准测试函数
Table 2. Standard test functions
函数 维度 搜索范围 最优解 ${f}_{1}(g)\text{=}{\displaystyle \sum _{r=1}^{n}{g}_{r}^{2} }$ 30 [−100，100] 0 ${f_2}(g) =\displaystyle \sum\limits_{r = 1}^n {\left| { {g_r} } \right|} + \prod\limits_{r = 1}^n {\left| { {g_r} } \right|}$ 30 [−10，10] 0 ${f_3}(g) = \displaystyle \sum\limits_{r = 1}^n {(\sum\limits_{q = 1}^n { {g_q}{)^2} } }$ 30 [−100，100] 0 $\mathop f\nolimits_4 (g) = \max \{ \left| {\mathop g\nolimits_r } \right|,1 \leqslant r \leqslant n\}$ 30 [−100，100] 0
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表 3 标准测试函数计算结果
Table 3. Calculation results of standard test functions
函数 PSO算法 EOPSO算法 CEOPSO算法 CEMOPSO算法 $ {f_1}(g) $ 标准差：$3.223\; 2 \times {10^{ { { - } }2} }$ 标准差：$ 6.193\;9 \times {10^{{{ - }}2}} $ 标准差：$2.925\;9 \times {10^{{{ - 6}}}}$ 标准差：$2.870\;6 \times {10^{{{ - 18}}}}$ 最优解：$ 2.807\;2 \times {10^{{{ - }}2}} $ 最优解：$ 2.979\;5 \times {10^{{{ - }}2}} $ 最优解：$1.393\;2 \times {10^{{{ - 6}}}}$ 最优解：$4.794\;3 \times {10^{{{ - 19}}}}$ $ {f_2}(g) $ 标准差：$ 1.001\;8 \times {10^0} $ 标准差：$ 1.255\;4 \times {10^0} $ 标准差：$ 7.436\;1 \times {10^{{{ - }}2}} $ 标准差：$5.045\;2 \times {10^{{{ - 13}}}}$ 最优解：$ 8.349\;6 \times {10^{{{ - }}1}} $ 最优解：$ 8.012\;2 \times {10^{{{ - }}1}} $ 最优解：$ 6.558\;2 \times {10^{{{ - }}2}} $ 最优解：$1.479\;4 \times {10^{{{ - 13}}}}$ $ {f_3}(g) $ 标准差：$ 39.100\;3 \times {10^0} $ 标准差：$ 36.417\;4 \times {10^0} $ 标准差：$ 34.092\;9 \times {10^0} $ 标准差：$9.092\;9 \times {10^{{{ - }}2}}$ 最优解：$ 32.092\;9 \times {10^0} $ 最优解：$ 31.565\;9 \times {10^0} $ 最优解：$ 32.073\;7 \times {10^0} $ 最优解：$7.686\;5 \times {10^{{{ - }}2}}$ $ {f_4}(g) $ 标准差：$ 1.268\;5 \times {10^0} $ 标准差：$ 1.820\;8 \times {10^0} $ 标准差：$ 5.433\;3 \times {10^{{{ - }}1}} $ 标准差：$1.683\;6 \times {10^{{{ - 3}}}}$ 最优解：$ 1.167\;1 \times {10^0} $ 最优解：$ 1.035\;9 \times {10^0} $ 最优解：$ 5.398\;9 \times {10^{{{ - }}1}} $ 最优解：$1.327\;9 \times {10^{{{ - 3}}}}$
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